Multi-chimera states in a higher order network of FitzHugh–Nagumo oscillators

Multi-chimera states in a higher order network of FitzHugh–Nagumo oscillators

14 March 2024 | Zhen Wang, Mingshu Chen, Xiaojian Xi, Huaigu Tian, and Rui Yang
The paper investigates the impact of higher-order interactions on the emergence and characteristics of multi-chimera states in a network of FitzHugh–Nagumo (FHN) oscillators. Multi-chimera states are configurations where both coherent and incoherent oscillators coexist, with multiple sets of synchronized systems coexisting within the network. The study uses measures of incoherence and discontinuity to assess the phenomenon. Key findings include: 1. **Network Model**: The network consists of coupled FHN systems with non-local coupling, where the interactions are defined on both first-order and second-order links. 2. **Higher Order Interactions**: The inclusion of higher-order interactions (three-node interactions) enhances the likelihood of multi-chimera states and expands the region where these states occur. 3. **Synchronization and Incoherence**: Complete coherence is achieved with lower first-order coupling strength, while higher-order networks exhibit imperfect chimera and imperfect synchronization. 4. **Statistical Measures**: The strength of incoherence (SI) is used to detect and quantify the chimera state, providing insights into the network's collective behavior. The study highlights the importance of higher-order interactions in altering the dynamics of interconnected systems, particularly in the context of multi-chimera states, and suggests that these interactions can significantly influence the network's stability and synchronization patterns.The paper investigates the impact of higher-order interactions on the emergence and characteristics of multi-chimera states in a network of FitzHugh–Nagumo (FHN) oscillators. Multi-chimera states are configurations where both coherent and incoherent oscillators coexist, with multiple sets of synchronized systems coexisting within the network. The study uses measures of incoherence and discontinuity to assess the phenomenon. Key findings include: 1. **Network Model**: The network consists of coupled FHN systems with non-local coupling, where the interactions are defined on both first-order and second-order links. 2. **Higher Order Interactions**: The inclusion of higher-order interactions (three-node interactions) enhances the likelihood of multi-chimera states and expands the region where these states occur. 3. **Synchronization and Incoherence**: Complete coherence is achieved with lower first-order coupling strength, while higher-order networks exhibit imperfect chimera and imperfect synchronization. 4. **Statistical Measures**: The strength of incoherence (SI) is used to detect and quantify the chimera state, providing insights into the network's collective behavior. The study highlights the importance of higher-order interactions in altering the dynamics of interconnected systems, particularly in the context of multi-chimera states, and suggests that these interactions can significantly influence the network's stability and synchronization patterns.
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